Spectrum Of Primordial Gravitational Waves Research Articles

Is the spectrum of gravitational waves the \u201cHoly Grail\u201d of inflation?

It is often said that detecting a spectrum of primordial gravitational waves via observing B-mode polarization of the Cosmic Microwave Background is the “Holy Grail” of inflation. The purpose of this short note is to point out that it is indeed of immense scientific interest to search for a signal of gravitational waves in B-mode polarization. However, rather than proving that inflation is the right paradigm of early universe cosmology, a positive signal of direct primordial B-mode polarization might well be due to other sources than inflation. In fact, a careful characterization of the spectrum of B-mode polarization might even falsify the inflationary paradigm.

Primordial gravitational waves and the H0 -tension problem

We analyse the H0-tension problem in the context of models of the early universe that predict a blue tilted spectrum of primordial gravitational waves (GW's). By considering the GW's contribution, Neff^GW, to the effective number of relativistic degrees of freedom, Neff, and assuming standard particle physics, we discuss the effects of Neff^GW on the background expansion, especially the constraints on the Hubble parameter H0. We analyse three scenarios which take into account the contribution of Neff^GW and perform a statistical study using recent data of cosmic microwave background, baryon acoustic oscillation, the latest measurement of the local expansion rate, along with the LIGO constraints on the tensor to scalar ratio and the tensor index. For the models explored, we show that an additional contribution from the primordial GW's background to Neff does not solve but alleviate the current H0-tension problem.

Deconfinement transition effects on cosmological parameters and primordial gravitational waves spectrum

The cosmological evolution can be described in terms of directly measurable cosmological scalar parameters (deceleration $q$, jerk $j$, snap $s$, etc...) constructed out of high order derivatives of the scale factor. Their behavior at the critical temperature of the Quantum Chromodynamics (QCD) phase transition in early universe could be a specific tool to study the transition, analogously to the fluctuations of conserved charges in QCD. We analyze the effect of the crossover transition from quarks and gluons to hadrons in early universe on the cosmological scalars and on the gravitational wave spectrum, by using the recent lattice QCD equation of state and including the electroweak degrees of freedom and different models of dark matter. Near the transition the cosmological parameters follow the behavior of QCD trace anomaly and of the speed of sound of the entire system. The effects of deconfinement turn out to be more relevant for the modification of the primordial spectrum of gravitational waves and our complete analysis, based on lattice QCD simulations and on the hadron resonance gas below the critical temperature, refines previous results.

Gravitational waves in cold dark matter

We study the effects of cold dark matter on the propagation of gravitational waves of astrophysical and primordial origin. We show that the dominant effect of cold dark matter on gravitational waves from astrophysical sources is a small frequency dependent modification of the propagation speed of gravitational waves. However, the magnitude of the effect is too small to be detected in the near future. We furthermore show that the spectrum of primordial gravitational waves in principle contains detailed information about the properties of dark matter. However, depending on the wavelength, the effects are either suppressed because the dark matter is highly non-relativistic or because it contributes a small fraction of the energy density of the universe. As a consequence, the effects of cold dark matter on primordial gravitational waves in practice also appear too small to be detectable.

Primordial gravitational waves, precisely: the role of thermodynamics in the Standard Model

In this paper, we revisit the estimation of the spectrum of primordial gravitational waves originated from inflation, particularly focusing on the effect of thermodynamics in the Standard Model of particle physics. By collecting recent results of perturbative and non-perturbative analysis of thermodynamic quantities in the Standard Model, we obtain the effective degrees of freedom including the corrections due to non-trivial interaction properties of particles in the Standard Model for a wide temperature interval. The impact of such corrections on the spectrum of primordial gravitational waves as well as the damping effect due to free-streaming particles is investigated by numerically solving the evolution equation of tensor perturbations in the expanding universe. It is shown that the reevaluation of the effects of free-streaming photons and neutrinos gives rise to some additional damping features overlooked in previous studies. We also observe that the continuous nature of the QCD crossover results in a smooth spectrum for modes that reenter the horizon at around the epoch of the QCD phase transition. Furthermore, we explicitly show that the values of the effective degrees of freedom remain smaller than the commonly used value 106.75 even at temperature much higher than the critical temperature of the electroweak crossover, and that the amplitude of primordial gravitational waves at a frequency range relevant to direct detection experiments becomes \U0001d4aa(1) % larger than previous estimates that do not include such corrections. This effect can be relevant to future high-sensitivity gravitational wave experiments such as ultimate DECIGO. Our results on the temperature evolution of the effective degrees of freedom are made available as tabulated data and fitting functions, which can also be used in the analysis of other cosmological relics.

Gravitational wave signals and cosmological consequences of gravitational reheating

Reheating after inflation can proceed even if the inflaton couples to Standard Model (SM) particles only gravitationally. However, particle production during the transition between de-Sitter expansion and a decelerating Universe is rather inefficient and the necessity to recover the visible Universe leads to a non-standard cosmological evolution initially dominated by remnants of the inflaton field. We remain agnostic to the specific dynamics of the inflaton field and discuss a generic scenario in which its remnants behave as a perfect fluid with a general barotropic parameter w. Using CMB and BBN constraints we derive the allowed range of inflationary scales. We also show that this scenario results in a characteristic primordial Gravitational Wave (GW) spectrum which gives hope for observation in upcoming runs of LIGO as well as in other planned experiments.

Primordial gravitational waves amplification from causal fluids

We consider the evolution of the gravitational wave spectrum for super-Hubble modes in interaction with a relativistic fluid, which is regarded as an effective description of fluctuations in a light scalar minimally coupled field, during the earliest epoch of the radiation dominated era after the end of inflation. We obtain the initial conditions for gravitons and fluid from quantum fluctuations at the end of inflation, and assume instantaneous reheating. We model the fluid by using relativistic causal hydrodynamics. There are two dimensionful parameters, the relaxation time $\tau$ and temperature. In particular we study the interaction between gravitational waves and the non trivial tensor (spin 2) part of the fluid energy-momentum tensor. Our main result is that the new dimensionful parameter $\tau$ introduces a new relevant scale which distinguishes two kinds of super-Hubble modes. For modes with $H^{-1}<\lambda<\tau$ the fluid-graviton interaction increases the amplitude of the primordial gravitational wave spectrum at the electroweak transition by a factor of about $1.3$ with respect to the usual scale invariant spectrum.

What drove cosmic inflation?

Inflation is the leading paradigm for the early Universe. Not only it solves several major puzzles of the Hot Big Bang model, such as the flatness puzzle, the horizon puzzle, and so on, but it offers a natural mechanism to explain the origin of cosmic structures. The quantum fluctuations generated by the inflation field during inflation finally seeded the formation of large-scale structure and the anisotropies of cosmic microwave background observed today. The simplest setup of inflation is the so-called slow-roll inflation model in which the inflation in the early universe is supposed to be driven by the potential energy of inflation field, and ended when the potential became steep and the kinetic energy of inflation field became dominant. In order to solve the puzzles of the Hot Big Bang model, the inflation should last for 60 e-foldings at least, and then the potential of inflation field should be flat enough. On the other hand, since the energy density of the Universe during inflation is dominated by the potential of inflation field, the quantum fluctuations of inflation will finally generate the primordial density perturbations which seed the formation of large-scale structure and the anisotropies of cosmic microwave background radiation. Due to the almost un-evolving Hubble parameter during inflation, the inflation model predicts a nearly scale-invariant power spectrum of density perturbations which has been confirmed by observations at a high confidence level. In addition, the gravitational waves should be excited and finally generated a non-zero power spectrum of primordial gravitational waves. Unfortunately, up to now, the primordial gravitational waves have not been detected. However, the origin of the inflation field and how to embed the inflationary scenario into a fundamental theory are still open questions. In this sense, more studies and more observations are needed before we can finally answer what drove cosmic inflation.

Gaugid inflation

The spectrum of primordial gravitational waves is one of the most robust inflationary observables, often thought of as a direct probe of the energy scale of inflation. We present a simple model, where the dynamics controlling this observable is very different than in the standard paradigm of inflation. The model is based on a peculiar finite density phase—the magnetic gaugid—which stems from a highly non-linear effective theory of a triplet of abelian gauge fields. The gaugid extends the notion of homogeneous isotropic solid, in that its spectrum of fluctuations includes helicity-2 phonons. We show how, upon implementing the gaugid to drive inflation, the helicity-2 phonon mixes with the graviton, significantly affecting the size of the primordial tensor spectrum. The rest of the features of the theory, in particular the vector and scalar perturbations, closely resemble those of solid inflation.

Detectability of primordial gravitational waves produced in bouncing models

It is widely known that bouncing models with a dust hydrodynamical fluid satisfying ${c_s^2=p_d/\rho_d\approx 0}$, where $c_s, p_d, \rho_d$ are the sound velocity, pressure and energy density of the dust fluid, respectively, have almost scale invariant spectrum of scalar perturbations and negligible primordial gravitational waves. We investigate whether adding another fluid with $1/3 < \lambda = p/\rho < 1$, which should dominate near the bounce, can increase the amplitude of gravitational waves in the high frequency regime, turning them detectable in near future observations for such range of frequencies. Indeed, we show that the energy density of primordial gravitational waves is proportional to $k^{2(9\lambda-1)/(1+3\lambda)}$ for wavelengths which become bigger than the Hubble radius when this extra fluid dominates the background. Hence, as $\lambda \to 1$ (an almost stiff matter fluid), the energy density of primordial gravitational waves will increase faster in frequency, turning them potentially detectable at high frequencies. However, there is an extra factor $I_q(\lambda)$ in the amplitude which decreases exponentially with $\lambda$. The net effect of these two contributions turns the energy density of primordial gravitational waves not sufficiently big at high frequencies in order to be detected by present day or near future observations for models which satisfy the nucleosynthesis bounds and is symmetric with respect to the bounce. Hence, symmetric bouncing models where the background is dominated by a dust hydrodynamical fluid with small sound velocity, do not present any significant amount of primordial gravitational waves at any frequency range compatible with observations, even if there are other fields present in the model dominating the bounce phase. Any detection of such waves will then rule out this kind of models.

Probing the primordial universe with gravitational waves detectors

The spectrum of primordial gravitational waves (GWs), especially its tilt nT, carries significant information about the primordial universe. Combining recent aLIGO and Planck2015+BK14 data, we find that the current limit is nT=0.016+0.614−0.989 at 95% C.L. We also estimate the impacts of Einstein Telescope and LISA on constraining nT. Moreover, based on the effective field theory of cosmological perturbations, we make an attempt to confront some models of early universe scenarios, which produce blue-tilted GWs spectrum (nT>0), with the corresponding datasets.

Cosmic parity violation due to a flavor-space locked gauge field

A flavor-space locked gauge field is shown to behave like a birefringent medium, imparting a preferred left- or right-circular polarization onto gravitational waves. In a cosmological scenario, such a gauge field can cause a primordial spectrum of gravitational waves to develop a net handedness. The degree of chiral asymmetry depends on the wavelength, the abundance of the gauge field, and the strength of the gauge coupling. An asymmetry in the gravitational wave spectrum would be imprinted on the photon polarization pattern of the cosmic microwave background at last scattering. In this scenario, cosmic parity violation is written on the sky, as we predict nonzero correlation of the curl polarization with the temperature, as well as curl with gradient polarization. We compare this phenomena with parity violation in models of chiral gravity, in which the chiral asymmetry is primordial, and with models of quintessence cosmic birefringence, in which parity-violating correlations are induced along the line of sight.

Odd tensor modes from inflation

The existence of a primordial spectrum of gravitational waves is a generic prediction of inflation. Here, I will discuss under what conditions the coupling of a pseudoscalar inflaton to a U(1) gauge field can induce, in a two-step process, gravitational waves with unusual properties such as: (i) a net chirality, (ii) a blue spectrum, (iii) large non-Gaussianities even if the scalar perturbations are approximately Gaussian and (iv) being detectable in the (relatively) near future by ground-based gravitational interferometers.

Cosmological and astrophysical probes of vacuum energy

Vacuum energy changes during cosmological phase transitions and becomes relatively important at epochs just before phase transitions. For a viable cosmology the vacuum energy just after a phase transition must be set by the critical temperature of the next phase transition, which exposes the cosmological constant problem from a different angle. Here we propose to experimentally test the properties of vacuum energy under circumstances different from our current vacuum. One promising avenue is to consider the effect of high density phases of QCD in neutron stars. Such phases have different vacuum expectation values and a different vacuum energy from the normal phase, which can contribute an order one fraction to the mass of neutron stars. Precise observations of the mass of neutron stars can potentially yield information about the gravitational properties of vacuum energy, which can significantly affect their mass-radius relation. A more direct test of cosmic evolution of vacuum energy could be inferred from a precise observation of the primordial gravitational wave spectrum at frequencies corresponding to phase transitions. While traditional cosmology predicts steps in the spectrum determined by the number of degrees of freedom both for the QCD and electroweak phase transitions, an adjustment mechanism for vacuum energy could significantly change this. In addition, there might be other phase transitions where the effect of vacuum energy could show up as a peak in the spectrum.

Reheating and primordial gravitational waves in generalized Galilean genesis

Galilean genesis is an alternative to inflation, in which the universe starts expanding from Minkowski with the stable violation of the null energy condition. In this paper, we discuss how the early universe is reheated through the gravitational particle production at the transition from the genesis phase to the subsequent phase where the kinetic energy of the scalar field is dominant. We then study the consequences of gravitational reheating after Galilean genesis on the spectrum of primordial gravitational waves. The resultant spectrum is strongly blue, and at high frequencies Ωgw∝ f3 in terms of the energy density per unit logarithmic frequency. Though this cannot be detected in existing detectors, the amplitude can be as large as Ωgw∼ 10−12 at f∼ 100 MHz, providing a future test of the genesis scenario. The analysis is performed within the framework of generalized Galilean genesis based on the Horndeski theory, which enables us to derive generic formulas.

Forecasting sensitivity on tilt of power spectrum of primordial gravitational waves after Planck satellite

By taking into account the contamination of foreground radiations, we employ the Fisher matrix to forecast the future sensitivity on the tilt of power spectrum of primordial tensor perturbations for several ground-based (AdvACT, CLASS, Keck/BICEP3, Simons Array, SPT-3G), balloon-borne (EBEX, Spider) and satellite (CMBPol, COrE, LiteBIRD) experiments of B-mode polarizations. For the fiducial model nt=0, our results show that the satellite experiments give good sensitivity on the tensor tilt nt to the level σnt≲0.1 for r≳2×10−3, while the ground-based and balloon-borne experiments give worse sensitivity. By considering the BICEP2/Keck Array and Planck (BKP) constraint on the tensor-to-scalar ratio r, we see that it is impossible for these experiments to test the consistency relation nt=−r/8 in the canonical single-field slow-roll inflation models.

Cosmological consequences of classical flavor-space locked gauge field radiation

We propose a classical SU(2) gauge field in a flavor-space locked configuration as a species of radiation in the early universe, and show that it would have a significant imprint on a primordial stochastic gravitational wave spectrum. In the flavor-space locked configuration, the electric and magnetic fields of each flavor are parallel and mutually orthogonal to other flavors, with isotropic and homogeneous stress-energy. Due to the non-Abelian coupling, the gauge field breaks the symmetry between left- and right-circularly polarized gravitational waves. This broken chiral symmetry results in a unique signal: non-zero cross correlation of the cosmic microwave background temperature and polarization, $TB$ and $EB$, both of which should be zero in the standard, chiral symmetric case. We forecast the ability of current and future CMB experiments to constrain this model. Furthermore, a wide range of behavior is shown to emerge, depending on the gauge field coupling, abundance, and allocation into electric and magnetic field energy density. The fluctuation power of primordial gravitational waves oscillates back and forth into fluctuations of the gauge field. In certain cases, the gravitational wave spectrum is shown to be suppressed or amplified by up to an order of magnitude depending on the initial conditions of the gauge field.

Chiral imprint of a cosmic gauge field on primordial gravitational waves

A cosmological gauge field with isotropic stress-energy introduces parity violation into the behavior of gravitational waves. We show that a primordial spectrum of inflationary gravitational waves develops a preferred handedness, left- or right-circularly polarized, depending on the abundance and coupling of the gauge field during the radiation era. A modest abundance of the gauge field would induce parity-violating correlations of the cosmic microwave background temperature and polarization patterns that could be detected by current and future experiments.

Multiwavelength constraints on the inflationary consistency relation

We present the first attempt to use a combination of CMB, LIGO, and Pulsar Timing Array (PPTA) data to constrain both the tilt and the running of primordial tensor power spectrum through constraints on the gravitational wave energy density generated in the early universe. Combining measurements at different cosmological scales highlights how complementary data can be used to test the predictions of early universe models including the inflationary consistency relation. Current data prefer a slightly positive tilt (${n}_{t}=0.0{6}_{\ensuremath{-}0.89}^{+0.63}$) and a negative running (${n}_{t,\text{run}}&lt;\ensuremath{-}0.22$) for the tensor power spectrum spectrum. Interestingly, the addition of direct gravitational wave detector data alone puts strong bounds on the tensor-to-scalar ratio $r&lt;0.2$ since the large positive tensor tilt preferred by the Planck temperature power spectrum is no longer allowed. Adding the recently released BICEP2/KECK and Planck 353 GHz polarization cross-correlation data gives an even stronger bound $r&lt;0.1$. We comment on possible effects of a large positive tilt on the background expansion and show that depending on the assumptions regarding the UV cutoff (${k}_{\mathrm{UV}}/{k}_{*}=1{0}^{24}$) of the primordial spectrum of gravitational waves, the strongest bounds on ${n}_{t}=0.0{7}_{\ensuremath{-}0.80}^{+0.52}$ are derived from this effect.

BICEP2, non-Bunch–Davies and entanglement

BICEP2 result on the tensor to scalar ratio r indicates a blue tilt in the primordial gravitational wave spectrum. This blue tilt and the observed large value r=0.2 are difficult to accommodate within the single field inflationary scenarios under standard conditions. Non-Bunch–Davies vacuum states have been proposed as a possibility. Such vacua are known to lead to pathologies. In this note we point out that it is known that these states ought to be interpreted as excited/squeezed states built over the standard Bunch–Davies vacuum in order to avoid pathological issues. We discuss the associated entanglement properties due to de Sitter horizon, and how such an approach may be more natural in the context of inflation. In particular, we suggest to employ entanglement considerations in de Sitter background to study the nature and intrinsic properties of modified initial states.